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The ongoing progress in (nuclear) many-body theory is accompanied by anever-rising increase in complexity of the underlying formalisms used to solvethe stationary Schr\"odinger equation. The associated working equations at playin state-of-the-art ab initio nuclear many-body methods can be analyticallyreduced with respect to angular-momentum, i.e. $SU(2)$, quantum numberswhenever they are effectively employed in a symmetry-restricted context. Thecorresponding procedure constitutes a tedious and error-prone but yet anintegral part of the implementation of those many-body frameworks. Indeed, thissymmetry reduction is a key step to advance modern simulations to higheraccuracy since the use of symmetry-adapted tensors can decrease thecomputational complexity by orders of magnitude.  While attempts have been made in the past to automate the (anti-) commutationrules linked to Fermionic and Bosonic algebras at play in the derivation of theworking equations, there is no systematic account to achieve the same goal fortheir symmetry reduction. In this work, the first version of an automated toolperforming graph-theory-based angular-momentum reduction is presented. Takingthe symmetry-unrestricted expressions of a generic tensor network as an input,the code provides their angular-momentum-reduced form in an error-safe way in amatter of seconds. Several state-of-the-art many-body methods serve as examplesto demonstrate the generality of the approach and to highlight the potentialimpact on the many-body community.

Symmetry reduction of tensor networks in many-body theory I. Automated symbolic evaluation of $SU(2)$ algebra